Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
400 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #22586696 | C2 | semidirect |
| 5. #22586239 | C2 | semidirect |
| 6. #22586185 | C2 | semidirect |
| 7. C2×#330×C71 | C2 | semidirect |
| 197. C2×#330 | D71 | semidirect |
| 201. C71 | #9266 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599508 | 2 |
| #22597334 | 2 |
| #22586958 | 2 |
| #22586696 | 2 |
| #22586239 | 2 |
| #22586185 | 2 |
| C2×#330×C71 | 2 |
| #9266 | 71 |